OF THE MECHANICAL POWERS. 53 



LECTURE III. 



OF THE MECHANICAL POWERS. 



IF we consider bodies in motion, and compare them The 

 together, we may do this either with respect to the 

 quantities of matter they contain, or the velocities with " me- 

 which they are moved. The heavier any body is, the 

 greater is the power required either to move it or to 

 stop its motion : and again, the swifter it moves, the 

 greater is its force. So that the whole momentum, or 

 quantity of force of a moving body, is the result of its 

 quantity of matter multiplied by the velocity with which 

 it is moved. And when the products arising from the 

 multiplication of the particular quantities of matter in 

 any two bodies by their respective velocities are equal, 

 the momenta or entire forces are so too. Thus, suppose a 

 body, which we shall call A, to weigh forty pounds, and to 

 move at the rate of two miles in a minute ; and another 

 body, which we shall call B, to weigh only four pounds, 

 and to move twenty miles in a minute ; the entire forces 

 with which these two bodies would strike against any 

 obstacle would be equal to each other, and therefore it 

 would require equal powers to stop them. For forty 

 multiplied by two gives eighty, the force of the body A ; 

 and twenty multiplied by four gives eighty, the force of 

 the body B. 



Upon this easy principle depends the whole of me- 

 chanics : and it holds universally true, that when two 

 bodies are suspended on any machine, so as to act 

 contrary to each other ; if the machine be put into mo- 

 tion, and the perpendicular ascent of one body multi- 

 plied into its weight, be equal to the perpendicular de- 

 scent of the other body multiplied into its weight, these 



